Lens assembly

ABSTRACT

A lens assembly includes a first lens, a second lens, a third lens, and a fourth lens, wherein the first lens, the second lens, the third lens, and the fourth lens are arranged in order from an object side to an image side along an optical axis. The first lens is with positive refractive power and includes a convex surface facing the object side. The second lens is with negative refractive power and includes a concave surface facing the image side. The third lens is with refractive power and includes a convex surface facing the image side. The fourth lens is with refractive power. The lens assembly satisfies: FOV≤56°, wherein FOV is a field of view of the lens assembly.

BACKGROUND OF THE INVENTION Field of the Invention

The invention relates to a lens assembly.

Description of the Related Art

The current development trend of a lens assembly is toward miniaturization. Additionally, the lens assembly is developed to have small field of view and high resolution capability in accordance with different application requirements. However, the known lens assembly can't satisfy such requirements. Therefore, the lens assembly needs a new structure in order to meet the requirements of miniaturization, small field of view, and high resolution at the same time.

BRIEF SUMMARY OF THE INVENTION

The invention provides a lens assembly to solve the above problems. The lens assembly of the invention is provided with characteristics of a shortened total lens length, a smaller field of view, a higher resolution, and still has a good optical performance.

The lens assembly in accordance with an exemplary embodiment of the invention includes a first lens, a second lens, a third lens, and a fourth lens, wherein the first lens, the second lens, the third lens, and the fourth lens are arranged in order from an object side to an image side along an optical axis. The first lens is with positive refractive power and includes a convex surface facing the object side. The second lens is with negative refractive power and includes a concave surface facing the image side. The third lens is with refractive power and includes a convex surface facing the image side. The fourth lens is with refractive power. The lens assembly satisfies: FOV≤56°, wherein FOV is a field of view of the lens assembly.

In another exemplary embodiment, the third lens is with negative refractive power and the fourth lens is with positive refractive power.

In yet another exemplary embodiment, the first lens further includes a concave surface facing the image side, the second lens further includes a convex surface facing the object side, the third lens further includes a concave surface facing the object side, and the fourth lens includes a convex surface facing the object side and a concave surface facing the image side.

In another exemplary embodiment, the first lens further includes a concave surface facing the image side, the second lens further includes a convex surface facing the object side, the third lens further includes a concave surface facing the object side, and the fourth lens includes a convex surface facing the object side and a convex surface facing the image side.

In yet another exemplary embodiment, the lens assembly satisfies: −21.5≤(R₄₁−R₄₂)/(R₄₁+R₄₂), wherein R₄₁ is a radius of curvature of an object side surface of the fourth lens and R₄₂ is a radius of curvature of an image side surface of the fourth lens.

In another exemplary embodiment, the lens assembly further includes a stop disposed between the object side and the third lens, wherein the lens assembly satisfies: 4 mm<TTL−SL<9 mm, wherein TTL is an interval from the convex surface of the first lens to an image plane along the optical axis and SL is an interval from the convex surface of the first lens to the stop along the optical axis.

In yet another exemplary embodiment, the lens assembly satisfies: f₁+f₂<−1 mm, wherein f₁ is an effective focal length of the first lens and f₂ is an effective focal length of the second lens.

In another exemplary embodiment, the lens assembly satisfies: −4≤f₂/f≤0, wherein f₂ is an effective focal length of the second lens and f is an effective focal length of the lens assembly.

In yet another exemplary embodiment, the lens assembly satisfies: 25<V₁−V₂<38, wherein V₁ is an Abbe number of the first lens and V₂ is an Abbe number of the second lens.

In another exemplary embodiment, the lens assembly satisfies: −25 mm<f₂+f₄<−1.5 mm, wherein f₂ is an effective focal length of the second lens and f₄ is an effective focal length of the fourth lens.

The lens assembly in accordance with an exemplary embodiment of the invention includes a first lens, a second lens, a third lens, a fourth lens, a fifth lens, and a sixth lens, wherein the first lens, the second lens, the third lens, the fourth lens, the fifth lens, and the sixth lens are arranged in order from an object side to an image side along an optical axis. The first lens is with positive refractive power and includes a convex surface facing the object side. The second lens is with negative refractive power and includes a concave surface facing the image side. The third lens is with refractive power and includes a convex surface facing the image side. The fourth lens is with refractive power. The fifth lens is with refractive power. The sixth lens is with refractive power. The lens assembly satisfies: 2 mm<f₅+f₆<35 mm, wherein f₅ is an effective focal length of the fifth lens and f₆ is an effective focal length of the sixth lens.

In another exemplary embodiment, the third lens is with positive refractive power, the fourth lens is with negative refractive power, the fifth lens is with positive refractive power, and the sixth lens is with negative refractive power.

In yet another exemplary embodiment, the second lens further includes a concave surface facing the object side, the third lens further includes a convex surface facing the object side, the fourth lens is a biconcave lens, the fifth lens includes a convex surface facing the object side, and the sixth lens is a biconcave lens.

In another exemplary embodiment, the second lens further includes a concave surface facing the object side, the third lens further includes a convex surface facing the object side, the fourth lens is a biconcave lens, the fifth lens includes a concave surface facing the object side, and the sixth lens is a biconcave lens.

In yet another exemplary embodiment, the lens assembly satisfies: −21.5≤(R₄₁−R₄₂)/(R₄₁+R₄₂)≤3.5, wherein R₄₁ is a radius of curvature of an object side surface of the fourth lens and R₄₂ is a radius of curvature of an image side surface of the fourth lens.

In another exemplary embodiment, the lens assembly further includes a stop disposed between the object side and the third lens, wherein the lens assembly satisfies: 4 mm<TTL−SL<9 mm, wherein TTL is an interval from the convex surface of the first lens to an image plane along the optical axis and SL is an interval from the convex surface of the first lens to the stop along the optical axis.

In yet another exemplary embodiment, the lens assembly satisfies: f₁+f₂<−1 mm, wherein f₁ is an effective focal length of the first lens and f₂ is an effective focal length of the second lens.

In another exemplary embodiment, the lens assembly satisfies: −4≤f₂/f≤0, wherein f₂ is an effective focal length of the second lens and f is an effective focal length of the lens assembly.

In yet another exemplary embodiment, the lens assembly satisfies: 25<V₁−V₂<38, wherein V₁ is an Abbe number of the first lens and V₂ is an Abbe number of the second lens.

In another exemplary embodiment, the lens assembly satisfies: −25 mm<f₂+f₄<−1.5 mm, wherein f₂ is an effective focal length of the second lens and f₄ is an effective focal length of the fourth lens.

A detailed description is given in the following embodiments with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention can be more fully understood by reading the subsequent detailed description and examples with references made to the accompanying drawings, wherein:

FIG. 1 is a lens layout and optical path diagram of a lens assembly in accordance with a first embodiment of the invention;

FIG. 2A depicts a longitudinal spherical aberration of the lens assembly in accordance with the first embodiment of the invention;

FIG. 2B is an astigmatic field curves diagram of the lens assembly in accordance with the first embodiment of the invention;

FIG. 2C is a distortion diagram of the lens assembly in accordance with the first embodiment of the invention;

FIG. 3 is a lens layout and optical path diagram of a lens assembly in accordance with a second embodiment of the invention;

FIG. 4A depicts a longitudinal spherical aberration of the lens assembly in accordance with the second embodiment of the invention;

FIG. 4B is an astigmatic field curves diagram of the lens assembly in accordance with the second embodiment of the invention;

FIG. 4C is a distortion diagram of the lens assembly in accordance with the second embodiment of the invention;

FIG. 5 is a lens layout and optical path diagram of a lens assembly in accordance with a third embodiment of the invention;

FIG. 6A depicts a field curvature diagram of the lens assembly in accordance with the third embodiment of the invention;

FIG. 6B is a distortion diagram of the lens assembly in accordance with the third embodiment of the invention;

FIG. 6C is a modulation transfer function diagram of the lens assembly in accordance with the third embodiment of the invention;

FIG. 7 is a lens layout and optical path diagram of a lens assembly in accordance with a fourth embodiment of the invention;

FIG. 8A depicts a field curvature diagram of the lens assembly in accordance with the fourth embodiment of the invention;

FIG. 8B is a distortion diagram of the lens assembly in accordance with the fourth embodiment of the invention;

FIG. 8C is a modulation transfer function diagram of the lens assembly in accordance with the fourth embodiment of the invention;

FIG. 9 is a lens layout and optical path diagram of a lens assembly in accordance with a fifth embodiment of the invention;

FIG. 10A depicts a field curvature diagram of the lens assembly in accordance with the fifth embodiment of the invention;

FIG. 10B is a distortion diagram of the lens assembly in accordance with the fifth embodiment of the invention; and

FIG. 10C is a modulation transfer function diagram of the lens assembly in accordance with the fifth embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

The following description is made for the purpose of illustrating the general principles of the invention and should not be taken in a limiting sense. The scope of the invention is best determined by reference to the appended claims.

Referring to FIG. 1, FIG. 1 is a lens layout and optical path diagram of a lens assembly in accordance with a first embodiment of the invention. The lens assembly 1 includes a stop ST1, a first lens L11, a second lens L12, a third lens L13, a fourth lens L14, an optical filter OF1, and a cover glass CG1, all of which are arranged in order from an object side to an image side along an optical axis OA1. In operation, an image of light rays from the object side is formed at an image plane IMA1.

The first lens L11 is a meniscus lens with positive refractive power and made of glass material, wherein the object side surface S12 is a convex surface, the image side surface S13 is a concave surface, and both of the object side surface S12 and image side surface S13 are aspheric surfaces.

The second lens L12 is a meniscus lens with negative refractive power and made of plastic material, wherein the object side surface S14 is a convex surface, the image side surface S15 is a concave surface, and both of the object side surface S14 and image side surface S15 are aspheric surfaces.

The third lens L13 is a meniscus lens with negative refractive power and made of plastic material, wherein the object side surface S16 is a concave surface, the image side surface S17 is a convex surface, and both of the object side surface S16 and image side surface S17 are aspheric surfaces.

The fourth lens L14 is a meniscus lens with positive refractive power and made of plastic material, wherein the object side surface S18 is a convex surface, the image side surface S19 is a concave surface, and both of the object side surface S18 and image side surface S19 are aspheric surfaces.

Both of the object side surface S110 and image side surface S111 of the optical filter OF1 are plane surfaces.

Both of the object side surface S112 and image side surface S113 of the cover glass CG1 are plane surfaces.

In order to maintain excellent optical performance of the lens assembly in accordance with the first embodiment of the invention, the lens assembly 1 satisfies at least one of the following conditions: FOV1≤56°  (1) 4 mm<TTL1−SL1<9 mm  (2) f1₁ +f1₂<−1 mm  (3) −4≤f1₂ /f1≤0  (4) 25<V1₁ −V1₂<38  (5) −21.5≤(R1₄₁ −R1₄₂)/(R1₄₁ +R1₄₂)≤3.5  (6) −25 mm<f1₂ +f1₄<−1.5 mm  (7)

wherein FOV1 is a field of view in degree for the lens assembly 1, TTL1 is an interval from the object side surface S12 of the first lens L11 to the image plane IMA1 along the optical axis OA1, SL1 is an interval from the object side surface S12 of the first lens L11 to the stop ST1 along the optical axis OA1, f1 ₁ is an effective focal length of the first lens L11, f1 ₂ is an effective focal length of the second lens L12, f1 ₄ is an effective focal length of the fourth lens L14, f1 is an effective focal length of the lens assembly 1, V1 ₁ is an Abbe number of the first lens L11, V1 ₂ is an Abbe number of the second lens L12, R1 ₄₁ is a radius of curvature of the object side surface S18 of the fourth lens L14, and R1 ₄₂ is a radius of curvature of the image side surface S19 of the fourth lens L14.

By the above design of the lenses, stop ST1, and satisfies at least one of the conditions (1)-(7), the lens assembly 1 is provided with an effective shortened total lens length, an effective decreased field of view, an increased resolution, and an effective corrected aberration.

In order to achieve the above purposes and effectively enhance the optical performance, the lens assembly 1 in accordance with the first embodiment of the invention is provided with the optical specifications shown in Table 1, which include the effective focal length, F-number, total lens length, field of view, radius of curvature of each lens surface, thickness between adjacent surface, refractive index of each lens, Abbe number of each lens, and effective focal length of each lens. Table 1 shows that the effective focal length is equal to 5.4619 mm, F-number is equal to 4.5, total lens length is equal to 6.688 mm, and field of view is equal to 43.9779 degrees for the lens assembly 1 of the first embodiment of the invention.

TABLE 1 Effective Focal Length = 5.4619 mm F-number = 4.5 Total Lens Length = 6.688 mm Field of View = 43.9779 Degrees Radius of Effective Surface Curvature Thickness Focal Length Number (mm) (mm) Nd Vd (mm) Remark S11 ∞ 0.000 Stop ST1 S12 1.852 0.395 1.589 61.2 3.51310 The First Lens L11 S13 16.186 0.050 S14 2.591 0.500 1.636 23.9 −6.02370 The Second Lens L12 S15 1.429 1.578 S16 −0.853 0.500 1.636 23.9 −5.11500 The Third Lens L13 S17 −1.420 0.050 S18 2.103 1.030 1.535 55.7 4.1985 The Fourth Lens L14 S19 27.234 0.500 S110 ∞ 0.210 1.517 64.2 Optical Filter OF1 S111 ∞ 1.426 S112 ∞ 0.400 1.517 64.2 Cover Glass CG1 S113 ∞ 0.050

The aspheric surface sag z of each lens in table 1 can be calculated by the following formula: z=ch ²/{1+[1−(k+1)c ² h ²]^(1/2) }+Ah ⁴ +Bh ⁶ +Ch ⁸ +Dh ¹⁰ where c is curvature, h is the vertical distance from the lens surface to the optical axis, k is conic constant and A, B, C and D are aspheric coefficients.

In the first embodiment, the conic constant k and the aspheric coefficients A, B, C, D of each surface are shown in Table 2.

TABLE 2 Surface Number S12 S13 S14 S15 K −3.5527E−01   0.0000E+00 −1.6190E+00 −2.9888E−02 A   3.8319E−03 −8.7036E−03 −2.2288E−03 −5.4284E−02 B −4.7768E−03   1.7903E−05   6.5077E−03   6.2554E−03 C   0.0000E+00   6.5897E−03   1.1869E−04   8.6668E−03 D   0.0000E+00   0.0000E+00   7.0890E−05   9.8377E−03 Surface Number S16 S17 S18 S19 K −2.3851E+00 −2.1665E+00 −9.4074E+00   0.0000E+00 A −5.1997E−02 −1.2031E−02 −1.1391E−02 −2.9667E−02 B −2.0059E−02   2.2708E−03   4.4922E−03   3.3095E−03 C   3.5820E−02   5.3712E−03 −1.0136E−03   6.4504E−04 D −1.7535E−02 −2.0000E−03   1.1801E−04 −1.1033E−04

Table 3 shows the parameters and condition values for conditions (1)-(7). As can be seen from Table 3, the lens assembly 1 of the first embodiment satisfies the conditions (1)-(7).

TABLE 3 FOV1 43.9779 TTL1  6.688 mm SL 1 0 mm Degrees f1₁ 3.5131 mm f1₂ −6.02370 f1₄ 4.1985 mm mm f1 5.4619 mm V1₁ 61.2 V1₂ 23.9 R1₄₁  2.103 mm R1₄₂ 27.234 mm FOV1 43.9779 TTL1 − SL1  6.688 mm f1₁ + f1₂ −2.511 Degrees mm f1₂ + f1₄ −1.825 mm f1₂/f1 −1.103 V1₁ − V1₂ 37.3 (R1₄₁ − R1₄₂)/( R1₄₁ + R1₄₂) −0.857

By the above arrangements of the lenses and stop ST1, the lens assembly 1 of the first embodiment can meet the requirements of optical performance as seen in FIGS. 2A-2C, wherein FIG. 2A shows a longitudinal spherical aberration diagram of the lens assembly 1 in accordance with the first embodiment of the invention, FIG. 2B shows an astigmatic field curves diagram of the lens assembly 1 in accordance with the first embodiment of the invention, and FIG. 2C shows a distortion diagram of the lens assembly 1 in accordance with the first embodiment of the invention.

It can be seen from FIG. 2A that the longitudinal spherical aberration in the lens assembly 1 of the first embodiment ranges from −0.005 mm to 0.013 mm for the wavelength of 435.8300 nm, 546.0700 nm, and 656.2800 nm.

It can be seen from FIG. 2B that the astigmatic field curves of tangential direction and sagittal direction in the lens assembly 1 of the first embodiment ranges from −0.005 mm to 0.005 mm for the wavelength of 546.0700 nm.

It can be seen from FIG. 2C that the distortion in the lens assembly 1 of the first embodiment ranges from 0% to 0.5% for the wavelength of 546.0700 nm.

It is obvious that the longitudinal spherical aberration, the astigmatic field curves, and the distortion of the lens assembly 1 of the first embodiment can be corrected effectively. Therefore, the lens assembly 1 of the first embodiment is capable of good optical performance.

Referring to FIG. 3, FIG. 3 is a lens layout and optical path diagram of a lens assembly in accordance with a second embodiment of the invention. The lens assembly 2 includes a stop ST2, a first lens L21, a second lens L22, a third lens L23, a fourth lens L24, an optical filter OF2, and a cover glass CG2, all of which are arranged in order from an object side to an image side along an optical axis OA2. In operation, an image of light rays from the object side is formed at an image plane IMA2.

The first lens L21 is a meniscus lens with positive refractive power and made of glass material, wherein the object side surface S22 is a convex surface, the image side surface S23 is a concave surface, and both of the object side surface S22 and image side surface S23 are aspheric surfaces.

The second lens L22 is a meniscus lens with negative refractive power and made of plastic material, wherein the object side surface S24 is a convex surface, the image side surface S25 is a concave surface, and both of the object side surface S24 and image side surface S25 are aspheric surfaces.

The third lens L23 is a meniscus lens with negative refractive power and made of plastic material, wherein the object side surface S26 is a concave surface, the image side surface S27 is a convex surface, and both of the object side surface S26 and image side surface S27 are aspheric surfaces.

The fourth lens L24 is a biconvex lens with positive refractive power and made of plastic material, wherein the object side surface S28 is a convex surface, the image side surface S29 is a convex surface, and both of the object side surface S28 and image side surface S29 are aspheric surfaces.

Both of the object side surface S210 and image side surface S211 of the optical filter OF2 are plane surfaces.

Both of the object side surface S212 and image side surface S213 of the cover glass CG2 are plane surfaces.

In order to maintain excellent optical performance of the lens assembly in accordance with the second embodiment of the invention, the lens assembly 2 satisfies at least one of the following conditions: FOV2≤56°  (8) 4 mm<TTL2−SL2<9 mm  (9) f2₁ +f2₂<−1 mm  (10) −4≤f2₂ /f2≤0  (11) 25<V2₁ −V2₂<38  (12) −21.5≤(R2₄₁ −R2₄₂)/(R2₄₁ +R2₄₂)≤3.5  (13) −25 mm<f2₂ +f2₄<−1.5 mm  (14)

The definition of FOV2, TTL2, SL2, f2 ₁, f2 ₂, f2 ₄, f2, V2 ₁, V2 ₂, R2 ₄₁, and R2 ₄₂ are the same as that of FOV1, TTL1, SL1, f1 ₁, f1 ₂, f1 ₄, f1, V1 ₁, V1 ₂, R1 ₄₁, and R1 ₄₂ in the first embodiment, and is not described here again.

By the above design of the lenses, stop ST2, and satisfies at least one of the conditions (8)-(14), the lens assembly 2 is provided with an effective shortened total lens length, an effective decreased field of view, an increased resolution, and an effective corrected aberration.

In order to achieve the above purposes and effectively enhance the optical performance, the lens assembly 2 in accordance with the second embodiment of the invention is provided with the optical specifications shown in Table 4, which include the effective focal length, F-number, total lens length, field of view, radius of curvature of each lens surface, thickness between adjacent surface, refractive index of each lens, Abbe number of each lens, and effective focal length of each lens. Table 4 shows that the effective focal length is equal to 5.4246 mm, F-number is equal to 4.5, total lens length is equal to 7.412 mm, and field of view is equal to 44.0706 degrees for the lens assembly 2 of the second embodiment of the invention.

TABLE 4 Effective Focal Length = 5.4246 mm F-number = 4.5 Total Lens Length = 7.412 mm Field of View = 44.0706 Degrees Sur- Effective face Radius of Thick- Focal Num- Curvature ness Length ber (mm) (mm) Nd Vd (mm) Remark S21 ∞ −0.090 Stop ST2 S22 2.066 0.500 1.589 61.2 5.59480 The First Lens L21 S23 5.037 0.453 S24 2.097 0.300 1.636 23.9 −19.03600 The Second Lens L22 S25 1.688 0.682 S26 −0.635 0.300 1.636 23.9 −3.00140 The Third Lens L23 S27 −1.126 0.100 S28 2.442 1.006 1.535 55.7 2.8826 The Fourth Lens L24 S29 −3.585 0.500 S210 ∞ 0.210 1.517 64.2 Optical Filter OF2 S211 ∞ 3.001 S212 ∞ 0.400 1.517 Cover Glass CG2 S213 ∞ 0.050

The aspheric surface sag z of each lens in table 4 can be calculated by the following formula: z=ch ²/{1+[1−(k+1)c ² h ²]^(1/2) }+Ah ⁴ +Bh ⁶ +Ch ⁸ +Dh ¹⁰ where c is curvature, h is the vertical distance from the lens surface to the optical axis, k is conic constant and A, B, C and D are aspheric coefficients.

In the second embodiment, the conic constant k and the aspheric coefficients A, B, C, D of each surface are shown in Table 5.

TABLE 5 Surface Number S22 S23 S24 S25 K   3.0921E−03   0.0000E+00 −6.3202E+00 −1.8255E+00 A   6.7904E−03 −2.4248E−02 −1.2011E−02 −3.9700E−02 B −4.9964E−03 −2.4752E−03 −3.8126E−02   2.6612E−02 C −1.5750E−04 −1.6603E−02   9.0336E−03   2.3417E−03 D   0.0000E+00   0.0000E+00 −3.5095E−03 −1.2144E−03 Surface Number S26 S27 S28 S29 K −2.1224E+00 −2.8806E+00 −2.2729E+01   0.0000E+00 A −5.2106E−02   1.4819E−02 −1.7987E−02 −8.0327E−03 B   1.6977E−02   7.5686E−03   6.6630E−03   1.0811E−03 C   6.4081E−02   2.5693E−03 −2.7596E−03 −7.5699E−04 D −1.5156E−02 −3.5407E−03 −5.3512E−04 −7.3260E−05

Table 6 shows the parameters and condition values for conditions (8)-(14). As can be seen from Table 6, the lens assembly 2 of the second embodiment satisfies the conditions (8)-(14).

TABLE 6 FOV2 44.0706 TTL2   7.412 mm SL2 0.09 mm Degrees f2₁ 5.5948 mm f2₂ −19.03600 f2₄ 2.8826 mm mm f2 5.4246 mm V2₁ 61.2 V2₂ 23.9 R2₄₁  2.442 mm R2₄₂ −3.582 mm FOV2 44.0706 TTL2 − SL2   7.322 mm f2₁ + f2₂ −13.4412 Degrees mm f2₂ + f2₄ −16.153 f2₂/f2 −3.509 V2₁ − V2₂ 37.3 mm (R2₄₁ − R2₄₂)/( R2₄₁ + R2₄₂) −5.274

By the above arrangements of the lenses and stop ST2, the lens assembly 2 of the second embodiment can meet the requirements of optical performance as seen in FIGS. 4A-4C, wherein FIG. 4A shows a longitudinal spherical aberration diagram of the lens assembly 2 in accordance with the second embodiment of the invention, FIG. 4B shows an astigmatic field curves diagram of the lens assembly 2 in accordance with the second embodiment of the invention, and FIG. 4C shows a distortion diagram of the lens assembly 2 in accordance with the second embodiment of the invention.

It can be seen from FIG. 4A that the longitudinal spherical aberration in the lens assembly 2 of the second embodiment ranges from 0.00 mm to 0.030 mm for the wavelength of 435.8300 nm, 546.0700 nm, and 656.2800 nm.

It can be seen from FIG. 4B that the astigmatic field curves of tangential direction and sagittal direction in the lens assembly 2 of the second embodiment ranges from −0.015 mm to 0.018 mm for the wavelength of 546.0700 nm.

It can be seen from FIG. 4C that the distortion in the lens assembly 2 of the second embodiment ranges from 0% to 1.3% for the wavelength of 546.0700 nm.

It is obvious that the longitudinal spherical aberration, the astigmatic field curves, and the distortion of the lens assembly 2 of the second embodiment can be corrected effectively. Therefore, the lens assembly 2 of the second embodiment is capable of good optical performance.

Referring to FIG. 5, FIG. 5 is a lens layout and optical path diagram of a lens assembly in accordance with a third embodiment of the invention. The lens assembly 3 includes a stop ST3, a first lens L31, a second lens L32, a third lens L33, a fourth lens L34, a fifth lens L35, a sixth lens L36, and an optical filter OF3, all of which are arranged in order from an object side to an image side along an optical axis OA3. In operation, an image of light rays from the object side is formed at an image plane IMA3.

The first lens L31 is a meniscus lens with positive refractive power and made of plastic material, wherein the object side surface S32 is a convex surface, the image side surface S33 is a concave surface, and both of the object side surface S32 and image side surface S33 are aspheric surfaces.

The second lens L32 is a biconcave lens with negative refractive power and made of plastic material, wherein the object side surface S34 is a concave surface, the image side surface S35 is a concave surface, and both of the object side surface S34 and image side surface S35 are aspheric surfaces.

The third lens L33 is a biconvex lens with positive refractive power and made of plastic material, wherein the object side surface S36 is a convex surface, the image side surface S37 is a convex surface, and both of the object side surface S36 and image side surface S37 are aspheric surfaces.

The fourth lens L34 is a biconcave lens with negative refractive power and made of plastic material, wherein the object side surface S38 is a concave surface, the image side surface S39 is a concave surface, and both of the object side surface S38 and image side surface S39 are aspheric surfaces.

The fifth lens L35 is a biconvex lens with positive refractive power and made of plastic material, wherein the object side surface S310 is a convex surface, the image side surface S311 is a convex surface, and both of the object side surface S310 and image side surface S311 are aspheric surfaces.

The sixth lens L36 is a biconcave lens with negative refractive power and made of plastic material, wherein the object side surface S312 is a concave surface, the image side surface S313 is a concave surface, and both of the object side surface S312 and image side surface S313 are aspheric surfaces

Both of the object side surface S314 and image side surface S315 of the optical filter OF3 are plane surfaces.

In order to maintain excellent optical performance of the lens assembly in accordance with the third embodiment of the invention, the lens assembly 3 satisfies at least one of the following conditions: FOV3≤56°  (15) 4 mm<TTL3−SL3<9 mm  (16) f3₁ −f3₂<−1 mm  (17) −25 mm<f3₂ +f3₄<−1.5 mm  (18) −4≤f3₂ /f3≤0  (19) 2 mm<f3₅ +f3₆<35 mm  (20) 25<V3₁ −V3₂<38  (21) −21.5≤(R3₄₁ −R3₄₂)/(R3₄₁ +R3₄₂)≤3.5  (22)

The definition of FOV3, TTL3, SL3, f3 ₁, f3 ₂, f3 ₄, f3, V3 ₁, V3 ₂, R3 ₄₁, and R3 ₄₂ are the same as that of FOV1, TTL1, SL1, f1 ₁, f1 ₂, f1 ₄, f1, V1 ₁, V1 ₂, R1 ₄₁, and R1 ₄₂ in the first embodiment, and is not described here again. f3 ₅ is an effective focal length of the fifth lens L35 and f3 ₆ is an effective focal length of the sixth lens L36.

By the above design of the lenses, stop ST3, and satisfies at least one of the conditions (15)-(22), the lens assembly 3 is provided with an effective shortened total lens length, an effective decreased field of view, an increased resolution, and an effective corrected aberration.

In order to achieve the above purposes and effectively enhance the optical performance, the lens assembly 3 in accordance with the third embodiment of the invention is provided with the optical specifications shown in Table 7, which include the effective focal length, F-number, total lens length, field of view, radius of curvature of each lens surface, thickness between adjacent surface, refractive index of each lens, Abbe number of each lens, and effective focal length of each lens. Table 7 shows that the effective focal length is equal to 5.574 mm, F-number is equal to 2.8, total lens length is equal to 5.88 mm, and field of view is equal to 55.5 degrees for the lens assembly 3 of the third embodiment of the invention.

TABLE 7 Effective Focal Length = 5.574 mm F-number = 2.8 Total Lens Length = 5.88 mm Field of View = 55.5 Degrees Radius of Effective Surface Curvature Thickness Focal Length Number (mm) (mm) Nd Vd (mm) Remark S31 ∞ −0.316 Stop ST3 S32 1.7608 0.591 1.535 56.115 3.423 The First Lens L31 S33 38.585 0.026 S34 −2512.54 0.35 1.636 23.972 −6.364 The Second Lens L32 S35 4.064 0.6 S36 8.398 1.083 1.535 56.115 7.624 The Third Lens L33 S37 −7.599 0.159 S38 −5.616 0.266 1.544 56.093 −5.354 The Fourth Lens L34 S39 6.171 0.031 S310 4.21 0.777 1.535 56.115 6.588 The Fifth Lens L35 S311 −20.468 0.791 S312 −3.319 0.295 1.535 56.115 −3.847 The Sixth Lens L36 S313 5.609 0.345 S314 ∞ 0.21 1.517 64.167 Optical Filter OF3 S315 ∞ 0.396

The aspheric surface sag z of each lens in table 7 can be calculated by the following formula: z=ch ²/{1+[1−(k+1)c ² h ²]^(1/2) }+Ah ⁴ +Bh ⁶ +Ch ⁸ +Dh ¹⁰ +Eh ¹² +Fh ¹⁴ +Gh ¹⁶ where c is curvature, h is the vertical distance from the lens surface to the optical axis, k is conic constant and A, B, C, D, E, F and G are aspheric coefficients.

In the third embodiment, the conic constant k and the aspheric coefficients A, B, C, D, E, F, G of each surface are shown in Table 8.

TABLE 8 Surface k A B C Number D E F G S32 0.024   8.24E−03 −4.99E−03   8.59E−03 −4.32E−03 −4.69E−04 −2.01E−03 −1.12E−03 S33 0 −8.55E−03   8.54E−03   8.86E−03 1.05E−02 −1.84E−04 −2.31E−03 −1.12E−02 S34 0 −2.40E−02   2.59E−02   2.08E−02 1.46E−02 −8.56E−03 −5.08E−03 −1.09E−03 S35 −1.101 −9.52E−03   5.91E−02 −7.41E−03 3.23E−02 −1.01E−02 −2.66E−02   3.80E−02 S36 3.316 −3.62E−02 −1.80E−03   7.05E−03 1.08E−02 −5.64E−03 −1.37E−02   7.73E−03 S37 0 −1.12E−01   1.07E−02 −2.49E−02 −7.59E−03   8.03E−03   7.83E−03 −6.23E−03 S38 0 −5.86E−02 −2.50E−02 −9.50E−03 −5.81E−03 −3.53E−03 −1.59E−03   1.41E−03 S39 −0.904 −3.41E−02   1.26E−02   1.38E−03 −2.64E−03 −1.61E−03 −6.45E−04 −2.98E−04 S310 4.469 −6.85E−02   1.93E−02 −1.29E−02 1.03E−03   8.80E−04 −3.64E−04 −1.23E−08 S311 −1002.23   3.17E−02   6.87E−04 −3.47E−03 −5.00E−04   4.84E−05   1.45E−04 −2.39E−05 S312 1.759 −3.46E−02   4.98E−04   9.89E−03 −7.83E−04 −7.24E−04 −4.02E−05   4.00E−05 S313 −10.386 −6.64E−02   1.42E−02 −2.36E−03 2.26E−04 −1.74E−05 −5.58E−06   4.41E−07

Table 9 shows the parameters and condition values for conditions (15)-(22). As can be seen from Table 8, the lens assembly 3 of the third embodiment satisfies the conditions (15)-(22).

TABLE 9 FOV3 55.5 TTL3 5.88 mm SL3 0.316 Degrees mm f3₁    3.423 mm f3₂ −6.364 f3₄ −5.354 mm mm f3₅    6.588 mm f3₆ −3.847 f3   5.574 mm mm V3₁ 56.115 V3₂ 23.972 R3₄₁ −5.616 mm R3₄₂    6.171 mm FOV3 55.5 TTL3 − SL3 5.564 f3₁ + f3₂ −2.941 Degrees mm mm f3₂ + f3₄ −11.718 mm f3₂/f3 −1.142 f3₅ + f3₆   2.741 mm V3₁ − V3₂ 32.143 (R3₄₁ − R3₄₂)/(R3₄₁ + R3₄₂) −21.238

By the above arrangements of the lenses and stop ST3, the lens assembly 3 of the third embodiment can meet the requirements of optical performance as seen in FIGS. 6A-6C, wherein FIG. 6A shows a field curvature diagram of the lens assembly 3 in accordance with the third embodiment of the invention, FIG. 6B shows a distortion diagram of the lens assembly 3 in accordance with the third embodiment of the invention, and FIG. 6C shows a modulation transfer function diagram of the lens assembly 3 in accordance with the third embodiment of the invention.

It can be seen from FIG. 6A that the field curvature of tangential direction and sagittal direction in the lens assembly 3 of the third embodiment ranges from −0.06 mm to 0.05 mm for the wavelength of 0.439 μm, 0.546 μm, 0.573 μm, 0.587 μm, and 0.656 μm.

It can be seen from FIG. 6B that the distortion in the lens assembly 3 of the third embodiment ranges from 0% to 1.8% for the wavelength of 0.439 μm, 0.546 μm, 0.573 μm, 0.587 μm, and 0.656 μm.

It can be seen from FIG. 6C that the modulation transfer function of tangential direction and sagittal direction in the lens assembly 3 of the third embodiment ranges from 0.38 to 1.0 wherein the wavelength ranges from 0.4385 μm to 0.6563 μm, the fields respectively are 0.0000 mm, 0.5867 mm, 1.1734 mm, 1.4668 mm, 2.0535 mm, 2.6402 mm, and 2.9335 mm, and the spatial frequency ranges from 0 lp/mm to 125 lp/mm.

It is obvious that the field curvature and the distortion of the lens assembly 3 of the third embodiment can be corrected effectively, and the resolution of the lens assembly 3 of the third embodiment can meet the requirement. Therefore, the lens assembly 3 of the third embodiment is capable of good optical performance.

Referring to FIG. 7, FIG. 7 is a lens layout and optical path diagram of a lens assembly in accordance with a fourth embodiment of the invention. The lens assembly 4 includes a first lens L41, a stop ST4, a second lens L42, a third lens L43, a fourth lens L44, a fifth lens L45, a sixth lens L46, and an optical filter OF4, all of which are arranged in order from an object side to an image side along an optical axis OA4. In operation, an image of light rays from the object side is formed at an image plane IMA4.

The first lens L41 is a meniscus lens with positive refractive power and made of plastic material, wherein the object side surface S41 is a convex surface, the image side surface S42 is a concave surface, and both of the object side surface S41 and image side surface S42 are aspheric surfaces.

The second lens L42 is a biconcave lens with negative refractive power and made of plastic material, wherein the object side surface S43 is a concave surface, the image side surface S44 is a concave surface, and both of the object side surface S43 and image side surface S44 are aspheric surfaces.

The third lens L43 is a biconvex lens with positive refractive power and made of plastic material, wherein the object side surface S45 is a convex surface, the image side surface S46 is a convex surface, and both of the object side surface S45 and image side surface S46 are aspheric surfaces.

The fourth lens L44 is a biconcave lens with negative refractive power and made of plastic material, wherein the object side surface S47 is a concave surface, the image side surface S48 is a concave surface, and both of the object side surface S47 and image side surface S48 are aspheric surfaces.

The fifth lens L45 is a meniscus lens with positive refractive power and made of plastic material, wherein the object side surface S49 is a convex surface, the image side surface S410 is a concave surface, and both of the object side surface S49 and image side surface S410 are aspheric surfaces.

The sixth lens L46 is a biconcave lens with negative refractive power and made of plastic material, wherein the object side surface S411 is a concave surface, the image side surface S412 is a concave surface, and both of the object side surface S411 and image side surface S412 are aspheric surfaces

Both of the object side surface S413 and image side surface S414 of the optical filter OF4 are plane surfaces.

In order to maintain excellent optical performance of the lens assembly in accordance with the fourth embodiment of the invention, the lens assembly 4 satisfies at least one of the following conditions: FOV4≤56°  (23) 4 mm<TTL4−SL4<9 mm  (24) f4₁ +f4₂<−1 mm  (25) −25 mm<f4₂ +f4₄<−1.5 mm  (26) −4≤f4₂ /f4≤0  (27) 2 mm<f4₅ +f4₆<35 mm  (28) 25<V4₁ −V4₂<38  (29) −21.5≤(R4₄₁ −R4₄₂)/(R4₄₁ +R4₄₂)≤3.5  (30)

The definition of FOV4, TTL4, SL4, f4 ₁, f4 ₂, f4 ₄, f4 ₅, f4 ₆, f4, V4 ₁, V4 ₂, R4 ₄₁, and R4 ₄₂ are the same as that of FOV3, TTL3, SL3, f3 ₁, f3 ₂, f3 ₄, f3 ₅, f3 ₆, f3, V3 ₁, V3 ₂, R3 ₄₁, and R3 ₄₂ in the third embodiment, and is not described here again.

By the above design of the lenses, stop ST4, and satisfies at least one of the conditions (23)-(30), the lens assembly 4 is provided with an effective shortened total lens length, an effective decreased field of view, an increased resolution, and an effective corrected aberration.

In order to achieve the above purposes and effectively enhance the optical performance, the lens assembly 4 in accordance with the fourth embodiment of the invention is provided with the optical specifications shown in Table 10, which include the effective focal length, F-number, total lens length, field of view, radius of curvature of each lens surface, thickness between adjacent surface, refractive index of each lens, Abbe number of each lens, and effective focal length of each lens. Table 10 shows that the effective focal length is equal to 7.082 mm, F-number is equal to 2.8, total lens length is equal to 7.7 mm, and field of view is equal to 45 degrees for the lens assembly 4 of the fourth embodiment of the invention.

TABLE 10 Effective Focal Length = 7.082 mm F-number = 2.8 Total Lens Length = 7.7 mm Field of View = 45 Degrees Radius of Effective Focal Surface Curvature Thickness Length Number (mm) (mm) Nd Vd (mm) Remark S41 2.347197 0.910177 1.535 56.115 4.547 The First Lens L41 S42 54.93809 0.046326 Stop ST4 S43 −20.1212 0.249992 1.636 23.972 −7.392 The Second Lens L42 S44 6.184075 0.108445 S45 7.374668 1.184192 1.535 56.115 9.335 The Third Lens L43 S46 −14.6877 0.274388 S47 −11.0451 0.913223 1.544 56.093 −6.845 The Fourth Lens L44 S48 5.799714 0.02497 S49 4.304854 1.69802 1.535 56.115 9.369 The Fifth Lens L45 S410 26.00662 1.176473 S411 −3.46793 0.309922 1.535 56.115 −4.533 The Sixth Lens L46 S412 8.369748 0.4 S413 ∞ 0.21 1.517 64.167 Optical Filter OF4 S414 ∞ 0.195235

The aspheric surface sag z of each lens in table 10 can be calculated by the following formula: z=ch ²/{1+[1−(k+1)c ² h ²]^(1/2) }+Ah ⁴ +Bh ⁶ +Ch ⁸ +Dh ¹⁰ +Eh ¹² +Fh ¹⁴ +Gh ¹⁶ where c is curvature, h is the vertical distance from the lens surface to the optical axis, k is conic constant and A, B, C, D, E, F and G are aspheric coefficients.

In the fourth embodiment, the conic constant k and the aspheric coefficients A, B, C, D, E, F, G of each surface are shown in Table 11.

TABLE 11 Surface k A B C Number D E F G S41 0.024   1.76E−03 −3.29E−03   5.27E−03 −3.55E−03 −1.46E−03   1.76E−03 −4.44E−04 S42 0   2.24E−02   4.43E−03 −4.83E−03 6.44E−03   1.79E−04 −3.88E−03   2.56E−04 S43 0   9.51E−03   1.78E−02   1.17E−02 −2.62E−03 −4.35E−03   1.77E−03 −1.16E−03 S44 −1.101 −1.02E−02   5.70E−02 −1.67E−03 1.29E−02 −5.04E−03 −1.22E−02   5.30E−03 S45 3.316 −1.12E−02   1.43E−02   2.27E−02 −1.14E−02 −9.35E−03   4.35E−03 −2.56E−03 S46 0 −1.14E−01   4.02E−03 −3.38E−03 −2.41E−03 −1.00E−03   5.70E−03 −3.28E−03 S47 0 −1.66E−01 −1.16E−02   3.32E−02 −4.85E−03 −1.50E−02   9.61E−03 −4.51E−04 S48 −0.904 −3.12E−02   2.29E−02   1.67E−03 −4.93E−03 −8.00E−04   1.21E−03 −1.43E−04 S49 4.469   1.05E−02   1.80E−03 −4.87E−03 −7.58E−04   8.69E−05   3.40E−04 −9.80E−05 S410 −1002.23   2.79E−02 −4.18E−03   1.76E−03 −3.52E−04 −6.09E−05   2.60E−05 −1.55E−06 S411 1.759 −7.58E−02   2.53E−02 −3.34E−04 −1.07E−03 −9.58E−05   2.59E−05   1.15E−05 S412 −10.386 −5.33E−02   1.12E−02 −4.96E−04 −2.72E−04   3.17E−07   7.68E−06 −5.92E−07

Table 12 shows the parameters and condition values for conditions (23)-(30). As can be seen from Table 12, the lens assembly 4 of the fourth embodiment satisfies the conditions (23)-(30).

TABLE 12 FOV4 45 TTL4  7.7 mm SL4 0.910 Degrees mm f4₁ 4.547 mm f4₂ −7.392 f4₄ −6.845 mm mm f4₅ 9.369 mm f4₆ −4.533 f4 7.082 mm mm V4₁ 56.115 V4₂ 23.972 R4₄₁ −11.0451 mm R4₄₂ 5.799714 mm FOV4 45 TTL4 − SL4 6.79 mm f4₁ + f4₂ −2.845 Degrees mm f4₂ + f4₄ −14.237 f4₂/f4 −1.044 f4₅ + f4₆ 4.836 mm mm V4₁ − V4₂ 32.143 (R4₄₁ − R4₄₂)/( R4₄₁ + R4₄₂) 3.211

By the above arrangements of the lenses and stop ST4, the lens assembly 4 of the fourth embodiment can meet the requirements of optical performance as seen in FIGS. 8A-8C, wherein FIG. 8A shows a field curvature diagram of the lens assembly 4 in accordance with the fourth embodiment of the invention, FIG. 8B shows a distortion diagram of the lens assembly 4 in accordance with the fourth embodiment of the invention, and FIG. 8C shows a modulation transfer function diagram of the lens assembly 4 in accordance with the fourth embodiment of the invention.

It can be seen from FIG. 8A that the field curvature of tangential direction and sagittal direction in the lens assembly 4 of the fourth embodiment ranges from −0.03 mm to 0.05 mm for the wavelength of 0.439 μm, 0.546 μm, 0.573 μm, 0.587 μm, and 0.656 μm.

It can be seen from FIG. 8B that the distortion in the lens assembly 4 of the fourth embodiment ranges from 0% to 2.0% for the wavelength of 0.439 μm, 0.546 μm, 0.573 μm, 0.587 μm, and 0.656 μm.

It can be seen from FIG. 8C that the modulation transfer function of tangential direction and sagittal direction in the lens assembly 4 of the fourth embodiment ranges from 0.38 to 1.0 wherein the wavelength ranges from 0.4385 μm to 0.6563 μm, the fields respectively are 0.0000 mm, 0.5867 mm, 1.1734 mm, 1.4668 mm, 2.0535 mm, 2.6402 mm, and 2.9335 mm, and the spatial frequency ranges from 0 lp/mm to 125 lp/mm.

It is obvious that the field curvature and the distortion of the lens assembly 4 of the fourth embodiment can be corrected effectively, and the resolution of the lens assembly 4 of the fourth embodiment can meet the requirement. Therefore, the lens assembly 4 of the fourth embodiment is capable of good optical performance.

Referring to FIG. 9, FIG. 9 is a lens layout and optical path diagram of a lens assembly in accordance with a fifth embodiment of the invention. The lens assembly 5 includes a first lens L51, a second lens L52, a stop ST5, a third lens L53, a fourth lens L54, a fifth lens L55, a sixth lens L56, and an optical filter OF5, all of which are arranged in order from an object side to an image side along an optical axis OA5. In operation, an image of light rays from the object side is formed at an image plane IMA5.

The first lens L51 is a biconvex lens with positive refractive power and made of plastic material, wherein the object side surface S51 is a convex surface, the image side surface S52 is a convex surface, and both of the object side surface S51 and image side surface S52 are aspheric surfaces.

The second lens L52 is a biconcave lens with negative refractive power and made of plastic material, wherein the object side surface S53 is a concave surface, the image side surface S54 is a concave surface, and both of the object side surface S53 and image side surface S54 are aspheric surfaces.

The third lens L53 is a biconvex lens with positive refractive power and made of plastic material, wherein the object side surface S56 is a convex surface, the image side surface S57 is a convex surface, and both of the object side surface S56 and image side surface S57 are aspheric surfaces.

The fourth lens L54 is a biconcave lens with negative refractive power and made of plastic material, wherein the object side surface S58 is a concave surface, the image side surface S59 is a concave surface, and both of the object side surface S58 and image side surface S59 are aspheric surfaces.

The fifth lens L55 is a meniscus lens with positive refractive power and made of plastic material, wherein the object side surface S510 is a concave surface, the image side surface S511 is a convex surface, and both of the object side surface S510 and image side surface S511 are aspheric surfaces.

The sixth lens L56 is a biconcave lens with negative refractive power and made of plastic material, wherein the object side surface S512 is a concave surface, the image side surface S513 is a concave surface, and both of the object side surface S512 and image side surface S513 are aspheric surfaces

Both of the object side surface S514 and image side surface S515 of the optical filter OF5 are plane surfaces.

In order to maintain excellent optical performance of the lens assembly in accordance with the fifth embodiment of the invention, the lens assembly 5 satisfies at least one of the following conditions: FOV5≤56°  (31) 4 mm<TTL5−SL5<9 mm  (32) f5₁ +f5₂<−1 mm  (33) −25 mm<f5₂ +f5₄<−1.5 mm  (34) −4≤f5₂ /f5≤0  (35) 2 mm<f5₅ +f5₆<35 mm  (36) 25<V5₁ −V5₂<38  (37) −21.5≤(R5₄₁ −R5₄₂)/(R5₄₁ +R5₄₂)≤3.5  (38)

The definition of FOV5, TTL5, SL5, f5 ₁, f5 ₂, f5 ₄, f5 ₅, f5 ₆, f5, V5 ₁, V5 ₂, R5 ₄₁, and R5 ₄₂ are the same as that of FOV3, TTL3, SL3, f3 ₁, f3 ₂, f3 ₄, f3 ₅, f3 ₆, f3, V3 ₁, V3 ₂, R3 ₄₁, and R3 ₄₂ in the third embodiment, and is not described here again.

By the above design of the lenses, stop ST5, and satisfies at least one of the conditions (31)-(38), the lens assembly 5 is provided with an effective shortened total lens length, an effective decreased field of view, an increased resolution, and an effective corrected aberration.

In order to achieve the above purposes and effectively enhance the optical performance, the lens assembly 5 in accordance with the fifth embodiment of the invention is provided with the optical specifications shown in Table 13, which include the effective focal length, F-number, total lens length, field of view, radius of curvature of each lens surface, thickness between adjacent surface, refractive index of each lens, Abbe number of each lens, and effective focal length of each lens. Table 13 shows that the effective focal length is equal to 7.0767 mm, F-number is equal to 2.8, total lens length is equal to 7.533 mm, and field of view is equal to 45 degrees for the lens assembly 5 of the fifth embodiment of the invention.

TABLE 13 Effective Focal Length = 7.076 mm F-number = 2.8 Total Lens Length = 7.533 mm Field of View = 45 Degrees Radius of Effective Focal Surface Curvature Thickness Length Number (mm) (mm) Nd Vd (mm) Remark S51 2.341 2.13 1.535 56.115 4.275 The First Lens L51 S52 −73.615 0.04 S53 −351.363 0.48 1.661 28.800 −6.395 The Second Lens L52 S54 4.3 0.31 S55 ∞ 0.07 Stop ST5 S56 8.459 1.37 1.661 26.800 8.134 The Third Lens L53 S57 −13.970 0.21 S58 −7.870 0.39 1.661 24.700 −9.582 The Fourth Lens L54 S59 33.838 0.46 S510 −6.000 0.40 1.661 20.373 27.959 The Fifth Lens L55 S511 −4.655 0.24 S512 −6.795 0.50 1.661 20.373 −5.431 The Sixth Lens L56 S513 7.905 0.27 S514 ∞ 0.21 1.517 64.167 Optical Filter OF5 S515 ∞ 0.44

The aspheric surface sag z of each lens in table 13 can be calculated by the following formula: z=ch ²/{1+[1−(k+1)c ² h ²]^(1/2) }+Ah ⁴ +Bh ⁶ +Ch ⁸ +Dh ¹⁰ +Eh ¹² +Fh ¹⁴ +Gh ¹⁶ where c is curvature, h is the vertical distance from the lens surface to the optical axis, k is conic constant and A, B, C, D, E, F and G are aspheric coefficients.

In the fifth embodiment, the conic constant k and the aspheric coefficients A, B, C, D, E, F, G of each surface are shown in Table 14.

TABLE 14 Surface k A B C Number D E F G S51 −0.627   3.62E−03 −4.44E−04   2.79E−04 −8.98E−05   0.00E+00   0.00E+00   0.00E+00 S52 0 −1.91E−02   1.44E−02 −4.36E−03 3.99E−04   0.00E+00   0.00E+00   0.00E+00 S53 0 −2.79E−04   1.88E−02 −3.93E−03 6.12E−04   0.00E+00   0.00E+00   0.00E+00 S54 14.006 −8.88E−03   1.20E−02 −4.76E−03 −2.79E−03   0.00E+00   0.00E+00   0.00E+00 S56 0 −2.97E−02 −2.54E−02   5.65E−02 −2.84E−02 −8.93E−02   1.60E−01 −7.94E−02 S57 0 −1.69E−01   3.93E−02 −2.05E−02 1.68E−02   1.44E−02 −5.70E−03 −2.51E−03 S58 24.344 −2.12E−01   1.84E−02   1.70E−02 4.91E−02 −4.10E−03 −2.07E−02   5.78E−03 S59 488.898 −2.37E−02   1.75E−02 −8.86E−04 −1.91E−03   1.26E−03 −5.86E−04   1.01E−04 S510 −49.446   3.31E−02   1.62E−02 −2.43E−02 7.66E−03   1.45E−04 −6.97E−04   1.23E−04 S511 −25.672 −6.38E−03   1.08E−02 −7.99E−04 −7.18E−04   9.13E−05 −1.66E−05   4.43E−06 S512 −3.722 −5.61E−02   1.13E−02   5.35E−03 −9.31E−04 −2.79E−04   4.40E−05   1.08E−06 S513 4.931 −7.33E−02   2.37E−02 −5.01E−03 5.34E−04   8.33E−06 −1.03E−05   7.74E−07

Table 15 shows the parameters and condition values for conditions (31)-(38). As can be seen from Table 15, the lens assembly 5 of the fifth embodiment satisfies the conditions (31)-(38).

TABLE 15 FOV5 45 TTL5 7.533 SL5 2.960 Degrees mm mm f5₁ 4.275 mm f5₂ −6.395 f5₄ −9.582 mm mm f5₅ 27.959 f5₆ −5.431 f5 7.076 mm mm mm V5₁ 56.115 V5₂ 28.800 R5₄₁ −7.870 mm R5₄₂ 33.838 mm FOV5 45 TTL5 − SL5 4.573 f5₁ + f5₂ −2.12 Degrees mm mm f5₂ + f5₄ −15.977 f5₂/f5 −0.904 f5₅ + f5₆ 22.528 mm mm V5₁ − V5₂ 35.74 (R5₄₁ − R5₄₂)/ −1.606 (R5₄₁ + R5₄₂)

By the above arrangements of the lenses and stop ST5, the lens assembly 5 of the fifth embodiment can meet the requirements of optical performance as seen in FIGS. 10A-10C, wherein FIG. 10A shows a field curvature diagram of the lens assembly 5 in accordance with the fifth embodiment of the invention, FIG. 10B shows a distortion diagram of the lens assembly 5 in accordance with the fifth embodiment of the invention, and FIG. 10C shows a modulation transfer function diagram of the lens assembly 5 in accordance with the fifth embodiment of the invention.

It can be seen from FIG. 10A that the field curvature of tangential direction and sagittal direction in the lens assembly 5 of the fifth embodiment ranges from −0.035 mm to 0.035 mm for the wavelength of 0.436 μm, 0.546 μm, 0.573 μm, 0.587 μm, and 0.656 μm.

It can be seen from FIG. 10B that the distortion in the lens assembly 5 of the fifth embodiment ranges from −0.8% to 0.2% for the wavelength of 0.436 μm, 0.546 μm, 0.573 μm, 0.587 μm, and 0.656 μm.

It can be seen from FIG. 10C that the modulation transfer function of tangential direction and sagittal direction in the lens assembly 5 of the fifth embodiment ranges from 0.41 to 1.0 wherein the wavelength ranges from 0.4358 μm to 0.6563 μm, the fields respectively are 0.0000 mm, 0.5867 mm, 1.1734 mm, 1.4668 mm, 2.0535 mm, 2.6402 mm, and 2.9335 mm, and the spatial frequency ranges from 0 lp/mm to 120 lp/mm.

It is obvious that the field curvature and the distortion of the lens assembly 5 of the fifth embodiment can be corrected effectively, and the resolution of the lens assembly 5 of the fifth embodiment can meet the requirement. Therefore, the lens assembly 5 of the fifth embodiment is capable of good optical performance.

Referring to Table 16 and Table 17, Table 16 provides optical specifications in accordance with a sixth embodiment of the invention; Table 17 provides aspheric coefficients of each surface in Table 16.

The figure which depicts the lens layout diagram of the lens assembly in accordance with the sixth embodiment of the invention is similar to the figure which depicts the lens layout diagram of the lens assembly in accordance with the third embodiment of the invention, thus the figure which depicts the lens layout diagram of the lens assembly in accordance with the sixth embodiment of the invention is omitted.

Table 16 shows that the effective focal length is equal to 7.076 mm, F-number is equal to 2.8, total lens length is equal to 7.7533 mm, and field of view is equal to 45 degrees for the lens assembly of the sixth embodiment of the invention.

TABLE 16 Effective Focal Length = 7.076 mm F-number = 2.8 Total Lens Length = 7.7533 mm Field of View = 45 Degrees Effective Radius of Focal Surface Curvature Thickness Length Number (mm) (mm) Nd Vd (mm) Remark S61 ∞ −0.346 Stop ST6 S62 2.087953 0.684262 1.535218 56.11525 3.849 The First Lens L61 S63 −154.0975 0.150804 S64 −16.56542 0.324744 1.661342 28.8 −5.817 The Second Lens L62 S65 5.076681 0.065043 S66 7.150339 1.594457 1.661342 26.8 5.011 The Third Lens L63 S67 −3.914118 0.029974 S68 −5.237808 1.100006 1.661342 24.7 −7.414 The Fourth Lens L64 S69 89.06507 0.041966 S610 26.85975 1.238261 1.662342 20.3729 29.636 The Fifth Lens L65 S611 −72.18347 0.678644 S612 −13.26351 0.499951 1.661342 20.3729 −3.702 The Sixth Lens L66 S613 3.062019 0.27 S614 ∞ 0.21 1.5168 64.16734 Optical Filter OF6 S615 ∞ 0.437948

The aspheric surface sag z of each lens in table 16 can be calculated by the following formula: z=ch ²/{1+[1−(k+1)c ² h ²]^(1/2)}+Ah⁴ +Bh ⁶ +Ch ⁸ +Dh ¹⁰ +Eh ¹² +Fh ¹⁴ +Gh ¹⁶ where c is curvature, h is the vertical distance from the lens surface to the optical axis, k is conic constant and A, B, C, D, E, F and G are aspheric coefficients.

In the sixth embodiment, the conic constant k and the aspheric coefficients A, B, C, D, E, F, G of each surface are shown in Table 17.

TABLE 17 Surface K A B C Number D E F G S62 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S63 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S64 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S65 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S66 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S67 3.341941 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S68 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S69 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S610 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S611 −21025.33 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S612 36.54096 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 S613 −0.898173 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

The difference between the above sixth embodiment of the lens assembly and the third embodiment of the lens assembly is that the image side surface S63 of the first lens L61 is a convex surface for the sixth embodiment of the lens assembly, however, the image side surface S33 of the first lens L31 is a concave surface for the third embodiment of the lens assembly.

The above field curvature (figure is omitted) and distortion (figure is omitted) for the sixth embodiment of the lens assembly can be corrected effectively, and the resolution for the sixth embodiment of the lens assembly can meet the requirement. Therefore, the lens assembly of the sixth embodiment is capable of good optical performance.

While the invention has been described by way of example and in terms of the preferred embodiment(s), it is to be understood that the invention is not limited thereto. On the contrary, it is intended to cover various modifications and similar arrangements and procedures, and the scope of the appended claims therefore should be accorded the broadest interpretation so as to encompass all such modifications and similar arrangements and procedures. 

What is claimed is:
 1. A lens assembly comprising: a first lens which is with positive refractive power and comprises a convex surface facing an object side; a second lens which is with negative refractive power and comprises a concave surface facing an image side; a third lens which is with negative refractive power and comprises a convex surface facing the image side; and a fourth lens which is with positive refractive power; wherein the first lens, the second lens, the third lens, and the fourth lens are arranged in order from the object side to the image side along an optical axis; wherein the lens assembly satisfies: −25 mm<f ₂ +f ₄<−1.5 mm, wherein f₂ is an effective focal length of the second lens and f₄ is an effective focal length of the fourth lens.
 2. A lens assembly comprising: a first lens which is with positive refractive power and comprises a convex surface facing an object side and a concave surface facing an image side; a second lens which is with negative refractive power and comprises a convex surface facing the object side and a concave surface facing the image side; a third lens which is with negative refractive power and comprises a concave surface facing the object side and a convex surface facing the image side; and a fourth lens which is with refractive power and comprises a convex surface facing the object side and a concave surface facing the image side; wherein the first lens, the second lens, the third lens, and the fourth lens are arranged in order from the object side to the image side along an optical axis; wherein the lens assembly satisfies: −25 mm<f ₂ +f ₄<−1.5 mm, wherein f₂ is an effective focal length of the second lens and f₄ is an effective focal length of the fourth lens.
 3. A lens assembly comprising: a first lens which is with positive refractive power and comprises a convex surface facing an object side and a concave surface facing an image side; a second lens which is with negative refractive power and comprises a convex surface facing the object side and a concave surface facing the image side; a third lens which is with negative refractive power and comprises a concave surface facing the object side and a convex surface facing the image side; and a fourth lens which is with refractive power and comprises a convex surface facing the object side and a convex surface facing the image side; wherein the first lens, the second lens, the third lens, and the fourth lens are arranged in order from the object side to the image side along an optical axis; wherein the lens assembly satisfies: −25 mm<f ₂ +f ₄<−1.5 mm, wherein f₂ is an effective focal length of the second lens and f₄ is an effective focal length of the fourth lens.
 4. The lens assembly as claimed in claim 1, wherein the lens assembly satisfies: −21.5≤(R ₄₁ −R ₄₂)/(R ₄₁ +R ₄₂)≤3.5, wherein R₄₁ is a radius of curvature of an object side surface of the fourth lens and R₄₂ is a radius of curvature of an image side surface of the fourth lens.
 5. The lens assembly as claimed in claim 1, further comprising a stop disposed between the object side and the third lens, wherein the lens assembly satisfies: 4 mm<TTL−SL<9 mm, wherein TTL is an interval from the convex surface of the first lens to an image plane along the optical axis and SL is an interval from the convex surface of the first lens to the stop along the optical axis.
 6. The lens assembly as claimed in claim 1, wherein the lens assembly satisfies: f ₁ +f ₂<−1 mm, wherein f₁ is an effective focal length of the first lens and f₂ is an effective focal length of the second lens.
 7. The lens assembly as claimed in claim 1, wherein the lens assembly satisfies: −4≤f ₂ /f≤0, wherein f₂ is an effective focal length of the second lens and f is an effective focal length of the lens assembly.
 8. The lens assembly as claimed in claim 1, wherein the lens assembly satisfies: 25<V ₁ −V ₂<38, wherein V₁ is an Abbe number of the first lens and V₂ is an Abbe number of the second lens.
 9. The lens assembly as claimed in claim 1, wherein the lens assembly satisfies: FOV≤56°, wherein FOV is a field of view of the lens assembly.
 10. The lens assembly as claimed in claim 1, further comprising: a fifth lens which is with refractive power; and a sixth lens which is with refractive power; wherein the first lens, the second lens, the third lens, the fourth lens, the fifth lens, and the sixth lens are arranged in order from the object side to the image side along an optical axis; wherein the lens assembly satisfies: 2 mm<f ₅ +f ₆<35 mm, wherein f₅ is an effective focal length of the fifth lens and f₆ is an effective focal length of the sixth lens.
 11. The lens assembly as claimed in claim 10, wherein the fifth lens is with positive refractive power, and the sixth lens is with negative refractive power.
 12. The lens assembly as claimed in claim 10, wherein the second lens further comprises a concave surface facing the object side, the third lens further comprises a convex surface facing the object side, the fourth lens is a biconcave lens, the fifth lens comprises a convex surface facing the object side, and the sixth lens is a biconcave lens.
 13. The lens assembly as claimed in claim 10, wherein the second lens further comprises a concave surface facing the object side, the third lens further comprises a convex surface facing the object side, the fourth lens is a biconcave lens, the fifth lens comprises a concave surface facing the object side, and the sixth lens is a biconcave lens.
 14. The lens assembly as claimed in claim 12, wherein the lens assembly satisfies: −21.5≤(R ₄₁ −R ₄₂)/(R ₄₁ +R ₄₂)≤3.5, wherein R₄₁ is a radius of curvature of an object side surface of the fourth lens and R₄₂ is a radius of curvature of an image side surface of the fourth lens.
 15. The lens assembly as claimed in claim 11, further comprising a stop disposed between the object side and the third lens, wherein the lens assembly satisfies: 4 mm<TTL−SL<9 mm, wherein TTL is an interval from the convex surface of the first lens to an image plane along the optical axis and SL is an interval from the convex surface of the first lens to the stop along the optical axis.
 16. The lens assembly as claimed in claim 15, wherein the lens assembly satisfies: f ₁ +f ₂<−1 mm, −4≤f ₂ /f≤0, wherein f is an effective focal length of the lens assembly, f₁ is an effective focal length of the first lens and f₂ is an effective focal length of the second lens.
 17. The lens assembly as claimed in claim 11, wherein the lens assembly satisfies: 25<V ₁ −V ₂<38, wherein V₁ is an Abbe number of the first lens and V₂ is an Abbe number of the second lens.
 18. The lens assembly as claimed in claim 14, wherein the lens assembly satisfies: −25 mm<f ₂ +f ₄<−1.5 mm, wherein f₂ is an effective focal length of the second lens and f₄ is an effective focal length of the fourth lens.
 19. The lens assembly as claimed in claim 12, wherein the first lens further comprises a convex surface or a concave surface facing the image side and the fifth lens further comprises a convex surface or a concave surface facing the image side.
 20. The lens assembly as claimed in claim 13, wherein the first lens further comprises a convex surface facing the image side and the fifth lens further comprises a convex surface facing the image side. 